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Spherical Barycentric Coordinates
[article]

2006
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Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
*

We develop

doi:10.2312/sgp/sgp06/081-088
fatcat:52sn3674grd3xn7pbklkn6z4zi
*spherical**barycentric**coordinates*. ... Furthermore,*spherical**barycentric**coordinates*can be used for all applications where only planar*barycentric**coordinates*were available up to now. ... It follows that there is a bijection between planar*barycentric**coordinates*and*spherical**barycentric**coordinates*. ...##
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Whitney Forms for Spherical Triangles I: The Euler, Cagnoli, and Tuynman Area Formulas, Barycentric Coordinates, and Construction with the Exterior Calculus
[article]

2014
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arXiv
*
pre-print

We introduce the three

arXiv:1404.6592v1
fatcat:4fcgnsauuvaaldis5wbrzlwzly
*barycentric**coordinates*of a point within the*spherical*triangle as area ratios which sum to unity. ... The*barycentric**coordinates*are the Whitney 0-forms, scalar functions over the domain of the triangle associated with each vertex. ... The Whitney Forms of a*Spherical*Triangle Let λ A (X) = S A (X) S , λ B (X) = S B (X) S and λ C (X) = S C (X) S be the*barycentric**coordinates*of the point X interior to or on the boundary of ABC, such ...##
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Fast Normal Vector Compression with Bounded Error
[article]

2007
*
Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing
*

The second uses fixed-precision

doi:10.2312/sgp/sgp07/263-272
fatcat:4t6rlgrebzaifk7cx2w5rw2gku
*barycentric**coordinates*. For both, we provide fast (de)compression algorithms and a rigorous upper bound on compression error. ... We discuss the effects of base polyhedra on the error bound and suggest polyhedra derived from*spherical*coverings. ... The next two integers represent the u and v*barycentric**coordinates*. Since the*barycentric**coordinates*u, v and w sum to 1, there is no need to explicitly store w. ...##
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Generating N-point spherical configurations with low mesh ratios using spherical area coordinates
[article]

2021
*
arXiv
*
pre-print

The method extends Caspar-Klug icosahedral point-grids to non-icosahedral nets through the use of planar

arXiv:2107.11265v1
fatcat:b6ulwmwrsjdfvnsh7f27s524qa
*barycentric**coordinates*, which are subsequently interpreted as*spherical*area*coordinates*for*spherical*... This short contribution presents a method for generating N-point*spherical*configurations with low mesh ratios. ... Homogenizing with*spherical*area*coordinates*In order to improve the uniformity of the generated point sets, we can reinterpret the planar*barycentric**coordinates*as a form of*spherical**barycentric**coordinates*...##
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Deuteron States Model

2018
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Journal of Lasers Optics & Photonics
*

*Barycentrical*

*coordinates*are generated to determine a nucleons

*barycentre*[2] . 3. ... It is postulated that the weak and the

*spherical*,

*barycentrical*

*coordinates*of the strong nucleon interaction are in special relativistic motion towards one another. 5. ...

*Barycentrical*

*coordinates*are generated to determine a nucleons

*barycentre*[2] . 3. ...

##
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Mean value coordinates in 3D

2005
*
Computer Aided Geometric Design
*

Trivariate

doi:10.1016/j.cagd.2005.06.004
fatcat:ilqtnl7yrfh6picbhr2fgizavu
*barycentric**coordinates*can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. ... These*coordinates*generalize in a natural way a recently constructed set of*coordinates*for planar polygons, called mean value*coordinates*. ... Clearly, for any p ∈T , we can express the vector e = p − v as e = τ i (e)e i + τ j (e)e j + τ k (e)e k , where τ i , τ j , τ k are the*spherical**barycentric**coordinates*of e. ...##
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Temporally-smooth Antialiasing and Lens Distortion with Rasterization Map
[article]

2020
*
arXiv
*
pre-print

To correct

arXiv:2010.04077v2
fatcat:lh6vkc3xqvcndbozatlezp2o2m
*barycentric*vector, rst distance pass ⃗ is obtained using inverse of the dot-product between*spherical*-*barycentric**coordinate*⃗ and the inversed vertex-distance vector. ...*Spherical*-*barycentric*vector ⃗ requires perspective-correction to be used as vertex-data interpolation weight. ...*coordinates*. xy , p o l y g [ 1 ] . xy ) , p o l y g [ 2 ] . xy ) −0.5 , 40 max ( max ( p o l y g [ 0 ] . xy , p o l y g [ 1 ] . xy ) , p o l y g [ 2 ] . xy ) +0.5 ) ; 41 } 42 / / Rasterize triangle ...##
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Interpolation on spherical geodesic grids: A comparative study

2007
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Journal of Computational and Applied Mathematics
*

Most operational models in atmospheric physics, meteorology and climatology nowadays adopt

doi:10.1016/j.cam.2006.10.068
fatcat:lhfmqjuu3jcahc3nw2e2zoff5i
*spherical*geodesic grids and require "ad hoc" developed interpolation procedures. ... (a) In [1]*spherical**barycentric**coordinates*(b 1 , b 2 , b 3 ) of a point P are introduced as the trihedral*coordinates*of its position vector v with respect to the trihedron generated by the position ... (d) In [15] the weights for the bilinear interpolation are the*barycentric**coordinates*evaluated in a local longitude-latitude*coordinate*system ( , ): if a point P ( , ) belongs to the*spherical*triangle ...##
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Inverse spherical surfaces

2005
*
Journal of Computational and Applied Mathematics
*

These surfaces can be seen as single-valued functions in

doi:10.1016/j.cam.2004.07.030
fatcat:ha4gvkmw55dpfk44j6vlh3yxqq
*spherical**coordinates*. ... In this paper we describe a new way to design rational parametric surfaces defined on*spherical*triangles which are useful for modelling in a*spherical*environment. ... We now can reinterpret Algorithm 2 as a de Casteljau algorithm which uses different (*spherical*)*barycentric**coordinates*for each sub-triangle T ( ) ij k instead of using the same*barycentric**coordinates*...##
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A Generic and Scalable Pipeline for GPU Tetrahedral Grid Rendering

2006
*
IEEE Transactions on Visualization and Computer Graphics
*

At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local

doi:10.1109/tvcg.2006.110
pmid:17080871
fatcat:hj2qjmwwmrdoxpmlokuicf34sm
*barycentric**coordinates*. ... This ray is sampled on a*spherical*slice with distance zs from the eye point. The*barycentric**coordinate*of the sample point is obtained by setting t as the depth of the actual*spherical*slice, zs. ... First, for every element the matrix required to transform eye*coordinates*into local*barycentric**coordinates*is computed. ...##
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Fundamentals of spherical parameterization for 3D meshes

2003
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ACM Transactions on Graphics
*

We describe a generalization of the method of

doi:10.1145/882262.882276
fatcat:pamhzygwvvdo3mm3g7yj2slogu
*barycentric**coordinates*for planar parameterization which solves the*spherical*parameterization problem, prove its correctness by establishing a connection ... Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the*spherical*triangles induced by the mesh connectivity are not ... Generalizing the*barycentric**coordinates*theory to*spherical*embeddings is not straightforward. ...##
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Fundamentals of spherical parameterization for 3D meshes

2003
*
ACM SIGGRAPH 2003 Papers on - SIGGRAPH '03
*

We describe a generalization of the method of

doi:10.1145/1201775.882276
fatcat:6qllnqlobjc2zgr7sorwknwyxq
*barycentric**coordinates*for planar parameterization which solves the*spherical*parameterization problem, prove its correctness by establishing a connection ... Parameterizing a triangle mesh onto the sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the*spherical*triangles induced by the mesh connectivity are not ... Generalizing the*barycentric**coordinates*theory to*spherical*embeddings is not straightforward. ...##
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Generalized barycentric coordinates and applications

2015
*
Acta Numerica
*

This paper surveys the construction, properties, and applications of generalized

doi:10.1017/s0962492914000129
fatcat:s53htignyjaofovbogwalrfbiq
*barycentric**coordinates*on polygons and polyhedra. ...*Spherical**coordinates**Spherical**barycentric**coordinates*for points in a*spherical*triangle were studied by Möbius (1846, Sec. 14) and Alfeld, Neamtu and Schumaker (1996) , and used in the latter to ... Unlike in the case of a planar triangle,*spherical**barycentric**coordinates*do not in general sum to 1. ...##
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Research on Goods and the Ship Interaction Based on ADAMS

2017
*
MATEC Web of Conferences
*

Figure 2 . 2

doi:10.1051/matecconf/20179511002
fatcat:ejoqfuwqgzfnncg5cmb25qbftq
*Barycentric**coordinates*curve. Figure 3 . 3*Barycentric**coordinates*curve.The rigid body under the constraint of*barycentre*trajectory is shown inFig. 4. ... Get the change of*barycentric**coordinates*as shown in Table 1: Table 1. ...##
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The Celestial Reference System in Relativistic Framework

1990
*
Symposium - International astronomical union
*

The concept of reference system, reference frame,

doi:10.1017/s0074180900086435
fatcat:urb36bg5q5fghfxeqcoszwdc3i
*coordinate*system and celestial sphere in a relativistic framework are given. ... The problems on the choice of celestial*coordinate*systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5. ... It is neither stationary nor*spherically*symmetric. ...
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